c = 299,792,458 + 0.158 m/s: Deriving the Speed of Light from the Fine-Structure Constant

We present a derivation of the speed of light requiring zero independent measurements of c and no reference to gravity. The derivation rests on a single chain: the fine-structure constant α is taken as a known quantity; the impedance of free space Z₀ = 4παℏ/e² then follows without reference to c; and the speed of light is recovered as c = Z₀/μ₀. Using the geometric value of α derived from the dimensional cascade of the OMEGA 137 framework (α⁻¹ = 137.035 999 086 288, an exact rational number agreeing with CODATA 2022 within 0.11σ), we obtain a physical speed of light c_phys = 299,792,458.158 m/s. The 0.158 m/s discrepancy from the SI-defined value is not error; it is the measurable signature of fixing c to a truncated empirical integer in 1983. The derivation replaces the empirical measurement of c with the algebraic determination of α, reducing the speed of light to a consequence of electromagnetic coupling strength and the dimensional projection of higher-dimensional geometry into observable 4D spacetime. This paper further argues that dimensionless constants are not devoid of dimensions but are operators encoding the collapse of many dimensions into a single scalar. The fine-structure constant α appears ubiquitously in physics precisely because it carries the geometric weight of every hidden dimension, selecting its operational meaning from context. We present testable predictions for precision geodesy.